Statistical Methods for Psychology

our actual difference with the minimum significant difference. This approach is frequently

taken by computer based post hoc procedures, such as those used by SPSS, so I cover it

here, but I really don’t find that it saves any time. Since

then

where is the minimum difference between two means that will be found to be

significant.

We know that with five means the critical value of. Then, for our data,

Thus, a difference in means equal to or greater than 8.14 would be judged significant,

whereas a smaller difference would not. Because the difference between the largest and

smallest means in the example is 25, we would reject.

Although qcould be used in place of an overall F(i.e., instead of running the tradi-

tional analysis of variance, we would test the difference between the two extreme means),

there is rarely an occasion to do so. In most cases, Fis more powerful than q. However,

where you expect several control group means to be equal to each other but different from

an experimental treatment mean (i.e., ), qmight well be the

more powerful statistic.

Although qis seldom a good substitute for the overall F, it is a very important statistic

when it comes to making multiple comparisons among individual treatment means. It

forms the basis for the next several tests.

Tukey’s Test

Much of the work on multiple comparisons has been based on the original work of Tukey,

and an important test bears his name.^11 The Tukey test,also called the Tukey’s HSD

(honestly significant difference) test or theWSD (wholly significant difference) test,

uses the Studentized qstatistic for its comparisons, except that is always taken as the

maximum value of. In other words, if there are five means, alldifferences are tested as if

they were five steps apart. The effect is to fix the familywise error rate at aagainst all pos-

sible null hypotheses, not just the complete null hypothesis, although with a loss of power.

The Tukey HSD is the favorite pairwise test for many people because of the control it exer-

cises over a.

If we apply the Tukey HSD to the data on morphine tolerance, we first arrange the

means in the order of increasing magnitude, as follows.

M-S M-M S-S S-M Mc-M

410112429

qr

qHSD

m 1 =m 2 =m 3 =m 4 Zm 5

H 0

X 12 Xs=4.07

A

32

8

=8.14

q.05(5,35)=4.07

X 12 Xs

X 12 Xs=q.05(r, dferror)

B

MSerror

n

qr=

X 12 Xs

B

MSerror

n

12.6 Post Hoc Comparisons 391

(^11) A second test (often referred to as the Tukey-btest), which is a modification on the HSD test, was proposed by
Tukey as less conservative. However, I have never seen it used and have omitted it from discussion.
Tukey test
Tukey’s HSD
(honestly signifi-
cant difference)
test
WSD (wholly
significant
difference) test